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In the xy-plane, line l intersects a circle with center at origin. Is the slope of line l equal to zero?
(1) Line l passes through second quadrant.
(2) Line l is perpendicular to the tangent of the circle.
(1) Line l passes through second quadrant.
(2) Line l is perpendicular to the tangent of the circle.
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19 Aug 2013, 12:04
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innocous
In the xy-plane , line l intersects a circle with center at origin.Is the slope of line l equal to zero?
1) line l passes through second quadrant.
2) line l is perpendicular to the tangent of the circle.
1) line l passes through second quadrant.
2) line l is perpendicular to the tangent of the circle.
ALL LINES WHICH ARE PERPENDICULAR TO TANGENT WILL PASS THROUGH CENTRE.
IMO C.
SEE DIAG FOR EXPLANATION.
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22 Aug 2013, 04:47
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In the xy-plane , line l intersects a circle with center at origin.Is the slope of line l equal to zero?
1) line l passes through second quadrant.
2) line l is perpendicular to the tangent of the circle.
FS1: Line l passing through second quadrant and intersecting the circle can be either parall to x-axis(in which case its slope is 0) or not parallel to x-axis(slope not eual to 0). Hence insufficient.
FS2: Line which is perpendicular to the tangent must pass thought centre (since angle betwwen radius and point of contact of tangent to a circle is 90 degrees). Hence, the line can have multiple possibilities for its slope (including 0 and infinity when the line is parallel to x or y axis respectively). Not sufficient.
Combining the above two, the only possibility is when the slope is negatice but not zero (x-axis is not in II quadrant). Hence slope iof line l is not zero for any case.
Sufficient. So answer should be C.
1) line l passes through second quadrant.
2) line l is perpendicular to the tangent of the circle.
FS1: Line l passing through second quadrant and intersecting the circle can be either parall to x-axis(in which case its slope is 0) or not parallel to x-axis(slope not eual to 0). Hence insufficient.
FS2: Line which is perpendicular to the tangent must pass thought centre (since angle betwwen radius and point of contact of tangent to a circle is 90 degrees). Hence, the line can have multiple possibilities for its slope (including 0 and infinity when the line is parallel to x or y axis respectively). Not sufficient.
Combining the above two, the only possibility is when the slope is negatice but not zero (x-axis is not in II quadrant). Hence slope iof line l is not zero for any case.
Sufficient. So answer should be C.
